It may be possible that both instances of MySQL are trying to record log entries to the same location (same file).
I do not think mysql allows more that one error log per MySQL instance.
Here is something further on using error log with mysqld and mysqld_safe:
No error log renaming occurs when the logs are flushed in any case if
the server is not writing to a named file.
If you use mysqld_safe to start mysqld, mysqld_safe arranges for
mysqld to write error messages to a log file or (as of MySQL 5.1.20)
• Before 5.1.20, mysqld_safe behavior is to log to a file, using the
default error log file if the --log-error option is not given to
mysqld_safe. Otherwise, mysqld_safe uses the file name specified using
• From 5.1.20 on, mysqld_safe has two additional error-logging
options, --syslog and --skip-syslog.
In 5.1.21 and up, the default with no logging options is
--skip-syslog, which is compatible with the default behavior of writing an error log file for releases prior to 5.1.20. To explicitly
specify use of an error log file, specify --log-error=file_name to
mysqld_safe, and mysqld_safe will arrange for mysqld to write messages
to a log file. To use syslog instead, specify the --syslog option.
In 5.1.20 only, the following conditions apply: 1) The default is to
use syslog, which is not compatible with releases prior to 5.1.20. 2)
Logging to syslog may fail to operate correctly in some cases; if so,
use --skip-syslog or --log-error.
For logging to syslog, messages from mysqld_safe and mysqld are
written with a tag of mysqld_safe and mysqld, respectively. As of
MySQL 5.1.21, to specify a suffix for the tag, use --syslog-tag=tag,
which modifies the tags to be mysqld_safe-tag and mysqld-tag.
If you specify --log-error in an option file in a section that mysqld
reads, mysqld_safe also will find and use the option.
Since you started mysqld_safe to start mysqld, you just need to start mysqld_safe and explicitly choose a separate file for the error of the other MySQL Instance using the -